Problem: Multiply and simplify the following complex numbers: $({-1-5i}) \cdot ({1-2i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-5i}) \cdot ({1-2i}) = $ $ ({-1} \cdot {1}) + ({-1} \cdot {-2i}) + ({-5i} \cdot {1}) + ({-5i} \cdot {-2i}) $ Then simplify the terms: $ (-1) + (2i) + (-5i) + (10i^2) $ Imaginary unit multiples can be grouped together. $ -1 + (2 - 5)i + 10 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -1 + (2 - 5)i - 10 $ The result is simplified: $ (-1 - 10) + (-3i) = -11-3i $